Propagator based formalism for optimizing in-line phase contrast imaging in laboratory X-ray setups

We derive a propagator based formalism for optimizing phase contrast imaging in laboratory setups as well as in synchrotron setups. We confirm based on five different setups the well known existence of an optimum position for the sample in terms of phase contrast by measuring two types of fibers and evaluating the fringe contrast. Furthermore, we demonstrate for these setups a correlation of our formula and the fringe contrast. Hence, an estimate of this optimum position is given by our formalism which only depends on the source size, the detector blurring, and the total distance between source and detector.